# Properties

 Label 1200.4.a.p.1.1 Level $1200$ Weight $4$ Character 1200.1 Self dual yes Analytic conductor $70.802$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1200.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$70.8022920069$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 120) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1200.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.00000 q^{3} +20.0000 q^{7} +9.00000 q^{9} +O(q^{10})$$ $$q-3.00000 q^{3} +20.0000 q^{7} +9.00000 q^{9} +56.0000 q^{11} +86.0000 q^{13} +106.000 q^{17} -4.00000 q^{19} -60.0000 q^{21} +136.000 q^{23} -27.0000 q^{27} -206.000 q^{29} +152.000 q^{31} -168.000 q^{33} -282.000 q^{37} -258.000 q^{39} -246.000 q^{41} +412.000 q^{43} +40.0000 q^{47} +57.0000 q^{49} -318.000 q^{51} +126.000 q^{53} +12.0000 q^{57} -56.0000 q^{59} -2.00000 q^{61} +180.000 q^{63} -388.000 q^{67} -408.000 q^{69} +672.000 q^{71} -1170.00 q^{73} +1120.00 q^{77} -408.000 q^{79} +81.0000 q^{81} +668.000 q^{83} +618.000 q^{87} +66.0000 q^{89} +1720.00 q^{91} -456.000 q^{93} +926.000 q^{97} +504.000 q^{99} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −3.00000 −0.577350
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 20.0000 1.07990 0.539949 0.841698i $$-0.318443\pi$$
0.539949 + 0.841698i $$0.318443\pi$$
$$8$$ 0 0
$$9$$ 9.00000 0.333333
$$10$$ 0 0
$$11$$ 56.0000 1.53497 0.767483 0.641069i $$-0.221509\pi$$
0.767483 + 0.641069i $$0.221509\pi$$
$$12$$ 0 0
$$13$$ 86.0000 1.83478 0.917389 0.397992i $$-0.130293\pi$$
0.917389 + 0.397992i $$0.130293\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 106.000 1.51228 0.756140 0.654409i $$-0.227083\pi$$
0.756140 + 0.654409i $$0.227083\pi$$
$$18$$ 0 0
$$19$$ −4.00000 −0.0482980 −0.0241490 0.999708i $$-0.507688\pi$$
−0.0241490 + 0.999708i $$0.507688\pi$$
$$20$$ 0 0
$$21$$ −60.0000 −0.623480
$$22$$ 0 0
$$23$$ 136.000 1.23295 0.616477 0.787373i $$-0.288559\pi$$
0.616477 + 0.787373i $$0.288559\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −27.0000 −0.192450
$$28$$ 0 0
$$29$$ −206.000 −1.31908 −0.659539 0.751671i $$-0.729248\pi$$
−0.659539 + 0.751671i $$0.729248\pi$$
$$30$$ 0 0
$$31$$ 152.000 0.880645 0.440323 0.897840i $$-0.354864\pi$$
0.440323 + 0.897840i $$0.354864\pi$$
$$32$$ 0 0
$$33$$ −168.000 −0.886214
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −282.000 −1.25299 −0.626493 0.779427i $$-0.715510\pi$$
−0.626493 + 0.779427i $$0.715510\pi$$
$$38$$ 0 0
$$39$$ −258.000 −1.05931
$$40$$ 0 0
$$41$$ −246.000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 412.000 1.46115 0.730575 0.682833i $$-0.239252\pi$$
0.730575 + 0.682833i $$0.239252\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 40.0000 0.124140 0.0620702 0.998072i $$-0.480230\pi$$
0.0620702 + 0.998072i $$0.480230\pi$$
$$48$$ 0 0
$$49$$ 57.0000 0.166181
$$50$$ 0 0
$$51$$ −318.000 −0.873116
$$52$$ 0 0
$$53$$ 126.000 0.326555 0.163278 0.986580i $$-0.447793\pi$$
0.163278 + 0.986580i $$0.447793\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 12.0000 0.0278849
$$58$$ 0 0
$$59$$ −56.0000 −0.123569 −0.0617846 0.998090i $$-0.519679\pi$$
−0.0617846 + 0.998090i $$0.519679\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.00419793 −0.00209897 0.999998i $$-0.500668\pi$$
−0.00209897 + 0.999998i $$0.500668\pi$$
$$62$$ 0 0
$$63$$ 180.000 0.359966
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −388.000 −0.707489 −0.353744 0.935342i $$-0.615092\pi$$
−0.353744 + 0.935342i $$0.615092\pi$$
$$68$$ 0 0
$$69$$ −408.000 −0.711847
$$70$$ 0 0
$$71$$ 672.000 1.12326 0.561632 0.827387i $$-0.310174\pi$$
0.561632 + 0.827387i $$0.310174\pi$$
$$72$$ 0 0
$$73$$ −1170.00 −1.87586 −0.937932 0.346818i $$-0.887262\pi$$
−0.937932 + 0.346818i $$0.887262\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1120.00 1.65761
$$78$$ 0 0
$$79$$ −408.000 −0.581058 −0.290529 0.956866i $$-0.593831\pi$$
−0.290529 + 0.956866i $$0.593831\pi$$
$$80$$ 0 0
$$81$$ 81.0000 0.111111
$$82$$ 0 0
$$83$$ 668.000 0.883404 0.441702 0.897162i $$-0.354375\pi$$
0.441702 + 0.897162i $$0.354375\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 618.000 0.761570
$$88$$ 0 0
$$89$$ 66.0000 0.0786066 0.0393033 0.999227i $$-0.487486\pi$$
0.0393033 + 0.999227i $$0.487486\pi$$
$$90$$ 0 0
$$91$$ 1720.00 1.98137
$$92$$ 0 0
$$93$$ −456.000 −0.508441
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 926.000 0.969289 0.484645 0.874711i $$-0.338949\pi$$
0.484645 + 0.874711i $$0.338949\pi$$
$$98$$ 0 0
$$99$$ 504.000 0.511656
$$100$$ 0 0
$$101$$ −198.000 −0.195067 −0.0975333 0.995232i $$-0.531095\pi$$
−0.0975333 + 0.995232i $$0.531095\pi$$
$$102$$ 0 0
$$103$$ −1532.00 −1.46556 −0.732779 0.680467i $$-0.761777\pi$$
−0.732779 + 0.680467i $$0.761777\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −444.000 −0.401150 −0.200575 0.979678i $$-0.564281\pi$$
−0.200575 + 0.979678i $$0.564281\pi$$
$$108$$ 0 0
$$109$$ 62.0000 0.0544819 0.0272409 0.999629i $$-0.491328\pi$$
0.0272409 + 0.999629i $$0.491328\pi$$
$$110$$ 0 0
$$111$$ 846.000 0.723412
$$112$$ 0 0
$$113$$ −414.000 −0.344653 −0.172327 0.985040i $$-0.555128\pi$$
−0.172327 + 0.985040i $$0.555128\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 774.000 0.611593
$$118$$ 0 0
$$119$$ 2120.00 1.63311
$$120$$ 0 0
$$121$$ 1805.00 1.35612
$$122$$ 0 0
$$123$$ 738.000 0.541002
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −996.000 −0.695911 −0.347956 0.937511i $$-0.613124\pi$$
−0.347956 + 0.937511i $$0.613124\pi$$
$$128$$ 0 0
$$129$$ −1236.00 −0.843595
$$130$$ 0 0
$$131$$ 264.000 0.176075 0.0880374 0.996117i $$-0.471941\pi$$
0.0880374 + 0.996117i $$0.471941\pi$$
$$132$$ 0 0
$$133$$ −80.0000 −0.0521570
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2278.00 −1.42060 −0.710302 0.703897i $$-0.751442\pi$$
−0.710302 + 0.703897i $$0.751442\pi$$
$$138$$ 0 0
$$139$$ −1812.00 −1.10570 −0.552848 0.833282i $$-0.686459\pi$$
−0.552848 + 0.833282i $$0.686459\pi$$
$$140$$ 0 0
$$141$$ −120.000 −0.0716725
$$142$$ 0 0
$$143$$ 4816.00 2.81632
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −171.000 −0.0959445
$$148$$ 0 0
$$149$$ −1534.00 −0.843424 −0.421712 0.906730i $$-0.638571\pi$$
−0.421712 + 0.906730i $$0.638571\pi$$
$$150$$ 0 0
$$151$$ 3016.00 1.62542 0.812711 0.582668i $$-0.197991\pi$$
0.812711 + 0.582668i $$0.197991\pi$$
$$152$$ 0 0
$$153$$ 954.000 0.504094
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 1814.00 0.922121 0.461060 0.887369i $$-0.347469\pi$$
0.461060 + 0.887369i $$0.347469\pi$$
$$158$$ 0 0
$$159$$ −378.000 −0.188537
$$160$$ 0 0
$$161$$ 2720.00 1.33147
$$162$$ 0 0
$$163$$ −1844.00 −0.886093 −0.443047 0.896499i $$-0.646102\pi$$
−0.443047 + 0.896499i $$0.646102\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 3768.00 1.74597 0.872984 0.487749i $$-0.162182\pi$$
0.872984 + 0.487749i $$0.162182\pi$$
$$168$$ 0 0
$$169$$ 5199.00 2.36641
$$170$$ 0 0
$$171$$ −36.0000 −0.0160993
$$172$$ 0 0
$$173$$ −938.000 −0.412224 −0.206112 0.978528i $$-0.566081\pi$$
−0.206112 + 0.978528i $$0.566081\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 168.000 0.0713427
$$178$$ 0 0
$$179$$ −3968.00 −1.65688 −0.828442 0.560075i $$-0.810772\pi$$
−0.828442 + 0.560075i $$0.810772\pi$$
$$180$$ 0 0
$$181$$ −3514.00 −1.44306 −0.721529 0.692384i $$-0.756560\pi$$
−0.721529 + 0.692384i $$0.756560\pi$$
$$182$$ 0 0
$$183$$ 6.00000 0.00242368
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 5936.00 2.32130
$$188$$ 0 0
$$189$$ −540.000 −0.207827
$$190$$ 0 0
$$191$$ 1480.00 0.560676 0.280338 0.959901i $$-0.409554\pi$$
0.280338 + 0.959901i $$0.409554\pi$$
$$192$$ 0 0
$$193$$ 2774.00 1.03460 0.517298 0.855806i $$-0.326938\pi$$
0.517298 + 0.855806i $$0.326938\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 3806.00 1.37648 0.688239 0.725484i $$-0.258384\pi$$
0.688239 + 0.725484i $$0.258384\pi$$
$$198$$ 0 0
$$199$$ 856.000 0.304926 0.152463 0.988309i $$-0.451280\pi$$
0.152463 + 0.988309i $$0.451280\pi$$
$$200$$ 0 0
$$201$$ 1164.00 0.408469
$$202$$ 0 0
$$203$$ −4120.00 −1.42447
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 1224.00 0.410985
$$208$$ 0 0
$$209$$ −224.000 −0.0741359
$$210$$ 0 0
$$211$$ −3020.00 −0.985334 −0.492667 0.870218i $$-0.663978\pi$$
−0.492667 + 0.870218i $$0.663978\pi$$
$$212$$ 0 0
$$213$$ −2016.00 −0.648517
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 3040.00 0.951008
$$218$$ 0 0
$$219$$ 3510.00 1.08303
$$220$$ 0 0
$$221$$ 9116.00 2.77470
$$222$$ 0 0
$$223$$ −1684.00 −0.505690 −0.252845 0.967507i $$-0.581366\pi$$
−0.252845 + 0.967507i $$0.581366\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 2004.00 0.585948 0.292974 0.956120i $$-0.405355\pi$$
0.292974 + 0.956120i $$0.405355\pi$$
$$228$$ 0 0
$$229$$ −5042.00 −1.45496 −0.727478 0.686131i $$-0.759307\pi$$
−0.727478 + 0.686131i $$0.759307\pi$$
$$230$$ 0 0
$$231$$ −3360.00 −0.957021
$$232$$ 0 0
$$233$$ 3090.00 0.868810 0.434405 0.900718i $$-0.356959\pi$$
0.434405 + 0.900718i $$0.356959\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 1224.00 0.335474
$$238$$ 0 0
$$239$$ −2136.00 −0.578102 −0.289051 0.957314i $$-0.593340\pi$$
−0.289051 + 0.957314i $$0.593340\pi$$
$$240$$ 0 0
$$241$$ 98.0000 0.0261939 0.0130970 0.999914i $$-0.495831\pi$$
0.0130970 + 0.999914i $$0.495831\pi$$
$$242$$ 0 0
$$243$$ −243.000 −0.0641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −344.000 −0.0886162
$$248$$ 0 0
$$249$$ −2004.00 −0.510033
$$250$$ 0 0
$$251$$ 5040.00 1.26742 0.633709 0.773571i $$-0.281532\pi$$
0.633709 + 0.773571i $$0.281532\pi$$
$$252$$ 0 0
$$253$$ 7616.00 1.89254
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1986.00 0.482036 0.241018 0.970521i $$-0.422519\pi$$
0.241018 + 0.970521i $$0.422519\pi$$
$$258$$ 0 0
$$259$$ −5640.00 −1.35310
$$260$$ 0 0
$$261$$ −1854.00 −0.439692
$$262$$ 0 0
$$263$$ 1416.00 0.331994 0.165997 0.986126i $$-0.446916\pi$$
0.165997 + 0.986126i $$0.446916\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −198.000 −0.0453835
$$268$$ 0 0
$$269$$ −6670.00 −1.51181 −0.755905 0.654681i $$-0.772803\pi$$
−0.755905 + 0.654681i $$0.772803\pi$$
$$270$$ 0 0
$$271$$ −48.0000 −0.0107594 −0.00537969 0.999986i $$-0.501712\pi$$
−0.00537969 + 0.999986i $$0.501712\pi$$
$$272$$ 0 0
$$273$$ −5160.00 −1.14395
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −6938.00 −1.50492 −0.752462 0.658636i $$-0.771134\pi$$
−0.752462 + 0.658636i $$0.771134\pi$$
$$278$$ 0 0
$$279$$ 1368.00 0.293548
$$280$$ 0 0
$$281$$ −1694.00 −0.359628 −0.179814 0.983701i $$-0.557550\pi$$
−0.179814 + 0.983701i $$0.557550\pi$$
$$282$$ 0 0
$$283$$ −6364.00 −1.33675 −0.668376 0.743824i $$-0.733010\pi$$
−0.668376 + 0.743824i $$0.733010\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −4920.00 −1.01191
$$288$$ 0 0
$$289$$ 6323.00 1.28699
$$290$$ 0 0
$$291$$ −2778.00 −0.559619
$$292$$ 0 0
$$293$$ 3134.00 0.624881 0.312441 0.949937i $$-0.398853\pi$$
0.312441 + 0.949937i $$0.398853\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −1512.00 −0.295405
$$298$$ 0 0
$$299$$ 11696.0 2.26220
$$300$$ 0 0
$$301$$ 8240.00 1.57789
$$302$$ 0 0
$$303$$ 594.000 0.112622
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −236.000 −0.0438737 −0.0219369 0.999759i $$-0.506983\pi$$
−0.0219369 + 0.999759i $$0.506983\pi$$
$$308$$ 0 0
$$309$$ 4596.00 0.846140
$$310$$ 0 0
$$311$$ −3776.00 −0.688480 −0.344240 0.938882i $$-0.611863\pi$$
−0.344240 + 0.938882i $$0.611863\pi$$
$$312$$ 0 0
$$313$$ 7918.00 1.42988 0.714939 0.699187i $$-0.246454\pi$$
0.714939 + 0.699187i $$0.246454\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −4362.00 −0.772853 −0.386426 0.922320i $$-0.626291\pi$$
−0.386426 + 0.922320i $$0.626291\pi$$
$$318$$ 0 0
$$319$$ −11536.0 −2.02474
$$320$$ 0 0
$$321$$ 1332.00 0.231604
$$322$$ 0 0
$$323$$ −424.000 −0.0730402
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −186.000 −0.0314551
$$328$$ 0 0
$$329$$ 800.000 0.134059
$$330$$ 0 0
$$331$$ −7980.00 −1.32514 −0.662569 0.749001i $$-0.730534\pi$$
−0.662569 + 0.749001i $$0.730534\pi$$
$$332$$ 0 0
$$333$$ −2538.00 −0.417662
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 8294.00 1.34066 0.670331 0.742062i $$-0.266152\pi$$
0.670331 + 0.742062i $$0.266152\pi$$
$$338$$ 0 0
$$339$$ 1242.00 0.198986
$$340$$ 0 0
$$341$$ 8512.00 1.35176
$$342$$ 0 0
$$343$$ −5720.00 −0.900440
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −964.000 −0.149136 −0.0745681 0.997216i $$-0.523758\pi$$
−0.0745681 + 0.997216i $$0.523758\pi$$
$$348$$ 0 0
$$349$$ 8670.00 1.32978 0.664892 0.746940i $$-0.268478\pi$$
0.664892 + 0.746940i $$0.268478\pi$$
$$350$$ 0 0
$$351$$ −2322.00 −0.353103
$$352$$ 0 0
$$353$$ 2314.00 0.348900 0.174450 0.984666i $$-0.444185\pi$$
0.174450 + 0.984666i $$0.444185\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −6360.00 −0.942876
$$358$$ 0 0
$$359$$ 1896.00 0.278738 0.139369 0.990240i $$-0.455493\pi$$
0.139369 + 0.990240i $$0.455493\pi$$
$$360$$ 0 0
$$361$$ −6843.00 −0.997667
$$362$$ 0 0
$$363$$ −5415.00 −0.782958
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1484.00 0.211074 0.105537 0.994415i $$-0.466344\pi$$
0.105537 + 0.994415i $$0.466344\pi$$
$$368$$ 0 0
$$369$$ −2214.00 −0.312348
$$370$$ 0 0
$$371$$ 2520.00 0.352647
$$372$$ 0 0
$$373$$ −12370.0 −1.71714 −0.858571 0.512694i $$-0.828648\pi$$
−0.858571 + 0.512694i $$0.828648\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −17716.0 −2.42021
$$378$$ 0 0
$$379$$ −5620.00 −0.761689 −0.380844 0.924639i $$-0.624367\pi$$
−0.380844 + 0.924639i $$0.624367\pi$$
$$380$$ 0 0
$$381$$ 2988.00 0.401784
$$382$$ 0 0
$$383$$ 5880.00 0.784475 0.392238 0.919864i $$-0.371701\pi$$
0.392238 + 0.919864i $$0.371701\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 3708.00 0.487050
$$388$$ 0 0
$$389$$ 2082.00 0.271367 0.135683 0.990752i $$-0.456677\pi$$
0.135683 + 0.990752i $$0.456677\pi$$
$$390$$ 0 0
$$391$$ 14416.0 1.86457
$$392$$ 0 0
$$393$$ −792.000 −0.101657
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1742.00 0.220223 0.110111 0.993919i $$-0.464879\pi$$
0.110111 + 0.993919i $$0.464879\pi$$
$$398$$ 0 0
$$399$$ 240.000 0.0301129
$$400$$ 0 0
$$401$$ −3270.00 −0.407222 −0.203611 0.979052i $$-0.565268\pi$$
−0.203611 + 0.979052i $$0.565268\pi$$
$$402$$ 0 0
$$403$$ 13072.0 1.61579
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −15792.0 −1.92329
$$408$$ 0 0
$$409$$ −6134.00 −0.741581 −0.370791 0.928716i $$-0.620913\pi$$
−0.370791 + 0.928716i $$0.620913\pi$$
$$410$$ 0 0
$$411$$ 6834.00 0.820186
$$412$$ 0 0
$$413$$ −1120.00 −0.133442
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 5436.00 0.638374
$$418$$ 0 0
$$419$$ 10392.0 1.21165 0.605826 0.795597i $$-0.292843\pi$$
0.605826 + 0.795597i $$0.292843\pi$$
$$420$$ 0 0
$$421$$ −12690.0 −1.46906 −0.734528 0.678578i $$-0.762596\pi$$
−0.734528 + 0.678578i $$0.762596\pi$$
$$422$$ 0 0
$$423$$ 360.000 0.0413801
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −40.0000 −0.00453334
$$428$$ 0 0
$$429$$ −14448.0 −1.62600
$$430$$ 0 0
$$431$$ 7408.00 0.827914 0.413957 0.910297i $$-0.364146\pi$$
0.413957 + 0.910297i $$0.364146\pi$$
$$432$$ 0 0
$$433$$ 5062.00 0.561811 0.280906 0.959735i $$-0.409365\pi$$
0.280906 + 0.959735i $$0.409365\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −544.000 −0.0595493
$$438$$ 0 0
$$439$$ 7160.00 0.778424 0.389212 0.921148i $$-0.372747\pi$$
0.389212 + 0.921148i $$0.372747\pi$$
$$440$$ 0 0
$$441$$ 513.000 0.0553936
$$442$$ 0 0
$$443$$ 17100.0 1.83396 0.916981 0.398930i $$-0.130618\pi$$
0.916981 + 0.398930i $$0.130618\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 4602.00 0.486951
$$448$$ 0 0
$$449$$ 8634.00 0.907491 0.453746 0.891131i $$-0.350087\pi$$
0.453746 + 0.891131i $$0.350087\pi$$
$$450$$ 0 0
$$451$$ −13776.0 −1.43833
$$452$$ 0 0
$$453$$ −9048.00 −0.938437
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −2986.00 −0.305644 −0.152822 0.988254i $$-0.548836\pi$$
−0.152822 + 0.988254i $$0.548836\pi$$
$$458$$ 0 0
$$459$$ −2862.00 −0.291039
$$460$$ 0 0
$$461$$ −2406.00 −0.243077 −0.121539 0.992587i $$-0.538783\pi$$
−0.121539 + 0.992587i $$0.538783\pi$$
$$462$$ 0 0
$$463$$ −14316.0 −1.43698 −0.718489 0.695538i $$-0.755166\pi$$
−0.718489 + 0.695538i $$0.755166\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −292.000 −0.0289339 −0.0144670 0.999895i $$-0.504605\pi$$
−0.0144670 + 0.999895i $$0.504605\pi$$
$$468$$ 0 0
$$469$$ −7760.00 −0.764016
$$470$$ 0 0
$$471$$ −5442.00 −0.532387
$$472$$ 0 0
$$473$$ 23072.0 2.24282
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 1134.00 0.108852
$$478$$ 0 0
$$479$$ −14056.0 −1.34078 −0.670391 0.742008i $$-0.733874\pi$$
−0.670391 + 0.742008i $$0.733874\pi$$
$$480$$ 0 0
$$481$$ −24252.0 −2.29895
$$482$$ 0 0
$$483$$ −8160.00 −0.768722
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −11204.0 −1.04251 −0.521254 0.853401i $$-0.674536\pi$$
−0.521254 + 0.853401i $$0.674536\pi$$
$$488$$ 0 0
$$489$$ 5532.00 0.511586
$$490$$ 0 0
$$491$$ −4608.00 −0.423536 −0.211768 0.977320i $$-0.567922\pi$$
−0.211768 + 0.977320i $$0.567922\pi$$
$$492$$ 0 0
$$493$$ −21836.0 −1.99482
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 13440.0 1.21301
$$498$$ 0 0
$$499$$ −2468.00 −0.221409 −0.110704 0.993853i $$-0.535311\pi$$
−0.110704 + 0.993853i $$0.535311\pi$$
$$500$$ 0 0
$$501$$ −11304.0 −1.00803
$$502$$ 0 0
$$503$$ 12192.0 1.08074 0.540372 0.841426i $$-0.318283\pi$$
0.540372 + 0.841426i $$0.318283\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −15597.0 −1.36625
$$508$$ 0 0
$$509$$ 1714.00 0.149257 0.0746284 0.997211i $$-0.476223\pi$$
0.0746284 + 0.997211i $$0.476223\pi$$
$$510$$ 0 0
$$511$$ −23400.0 −2.02574
$$512$$ 0 0
$$513$$ 108.000 0.00929496
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 2240.00 0.190551
$$518$$ 0 0
$$519$$ 2814.00 0.237998
$$520$$ 0 0
$$521$$ −18014.0 −1.51479 −0.757397 0.652955i $$-0.773529\pi$$
−0.757397 + 0.652955i $$0.773529\pi$$
$$522$$ 0 0
$$523$$ −16748.0 −1.40027 −0.700133 0.714013i $$-0.746876\pi$$
−0.700133 + 0.714013i $$0.746876\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 16112.0 1.33178
$$528$$ 0 0
$$529$$ 6329.00 0.520178
$$530$$ 0 0
$$531$$ −504.000 −0.0411897
$$532$$ 0 0
$$533$$ −21156.0 −1.71926
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 11904.0 0.956602
$$538$$ 0 0
$$539$$ 3192.00 0.255082
$$540$$ 0 0
$$541$$ −14018.0 −1.11401 −0.557006 0.830508i $$-0.688050\pi$$
−0.557006 + 0.830508i $$0.688050\pi$$
$$542$$ 0 0
$$543$$ 10542.0 0.833150
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −412.000 −0.0322045 −0.0161022 0.999870i $$-0.505126\pi$$
−0.0161022 + 0.999870i $$0.505126\pi$$
$$548$$ 0 0
$$549$$ −18.0000 −0.00139931
$$550$$ 0 0
$$551$$ 824.000 0.0637089
$$552$$ 0 0
$$553$$ −8160.00 −0.627484
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −18218.0 −1.38586 −0.692928 0.721007i $$-0.743679\pi$$
−0.692928 + 0.721007i $$0.743679\pi$$
$$558$$ 0 0
$$559$$ 35432.0 2.68088
$$560$$ 0 0
$$561$$ −17808.0 −1.34020
$$562$$ 0 0
$$563$$ 23524.0 1.76096 0.880478 0.474087i $$-0.157222\pi$$
0.880478 + 0.474087i $$0.157222\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 1620.00 0.119989
$$568$$ 0 0
$$569$$ 23330.0 1.71888 0.859442 0.511234i $$-0.170811\pi$$
0.859442 + 0.511234i $$0.170811\pi$$
$$570$$ 0 0
$$571$$ 13124.0 0.961860 0.480930 0.876759i $$-0.340299\pi$$
0.480930 + 0.876759i $$0.340299\pi$$
$$572$$ 0 0
$$573$$ −4440.00 −0.323706
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −11714.0 −0.845165 −0.422582 0.906324i $$-0.638876\pi$$
−0.422582 + 0.906324i $$0.638876\pi$$
$$578$$ 0 0
$$579$$ −8322.00 −0.597324
$$580$$ 0 0
$$581$$ 13360.0 0.953987
$$582$$ 0 0
$$583$$ 7056.00 0.501252
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −17628.0 −1.23950 −0.619749 0.784800i $$-0.712766\pi$$
−0.619749 + 0.784800i $$0.712766\pi$$
$$588$$ 0 0
$$589$$ −608.000 −0.0425335
$$590$$ 0 0
$$591$$ −11418.0 −0.794710
$$592$$ 0 0
$$593$$ 2802.00 0.194038 0.0970188 0.995283i $$-0.469069\pi$$
0.0970188 + 0.995283i $$0.469069\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −2568.00 −0.176049
$$598$$ 0 0
$$599$$ 2664.00 0.181716 0.0908582 0.995864i $$-0.471039\pi$$
0.0908582 + 0.995864i $$0.471039\pi$$
$$600$$ 0 0
$$601$$ 23962.0 1.62634 0.813170 0.582026i $$-0.197740\pi$$
0.813170 + 0.582026i $$0.197740\pi$$
$$602$$ 0 0
$$603$$ −3492.00 −0.235830
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 11940.0 0.798401 0.399201 0.916864i $$-0.369288\pi$$
0.399201 + 0.916864i $$0.369288\pi$$
$$608$$ 0 0
$$609$$ 12360.0 0.822418
$$610$$ 0 0
$$611$$ 3440.00 0.227770
$$612$$ 0 0
$$613$$ −16794.0 −1.10653 −0.553265 0.833005i $$-0.686618\pi$$
−0.553265 + 0.833005i $$0.686618\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 20706.0 1.35104 0.675520 0.737341i $$-0.263919\pi$$
0.675520 + 0.737341i $$0.263919\pi$$
$$618$$ 0 0
$$619$$ −10724.0 −0.696339 −0.348170 0.937432i $$-0.613197\pi$$
−0.348170 + 0.937432i $$0.613197\pi$$
$$620$$ 0 0
$$621$$ −3672.00 −0.237282
$$622$$ 0 0
$$623$$ 1320.00 0.0848871
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 672.000 0.0428024
$$628$$ 0 0
$$629$$ −29892.0 −1.89487
$$630$$ 0 0
$$631$$ 5744.00 0.362385 0.181193 0.983448i $$-0.442004\pi$$
0.181193 + 0.983448i $$0.442004\pi$$
$$632$$ 0 0
$$633$$ 9060.00 0.568883
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 4902.00 0.304905
$$638$$ 0 0
$$639$$ 6048.00 0.374421
$$640$$ 0 0
$$641$$ 27906.0 1.71953 0.859767 0.510687i $$-0.170609\pi$$
0.859767 + 0.510687i $$0.170609\pi$$
$$642$$ 0 0
$$643$$ 20556.0 1.26073 0.630365 0.776299i $$-0.282905\pi$$
0.630365 + 0.776299i $$0.282905\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −10224.0 −0.621247 −0.310624 0.950533i $$-0.600538\pi$$
−0.310624 + 0.950533i $$0.600538\pi$$
$$648$$ 0 0
$$649$$ −3136.00 −0.189675
$$650$$ 0 0
$$651$$ −9120.00 −0.549064
$$652$$ 0 0
$$653$$ 12982.0 0.777986 0.388993 0.921241i $$-0.372823\pi$$
0.388993 + 0.921241i $$0.372823\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −10530.0 −0.625288
$$658$$ 0 0
$$659$$ 1512.00 0.0893766 0.0446883 0.999001i $$-0.485771\pi$$
0.0446883 + 0.999001i $$0.485771\pi$$
$$660$$ 0 0
$$661$$ 16710.0 0.983273 0.491637 0.870800i $$-0.336399\pi$$
0.491637 + 0.870800i $$0.336399\pi$$
$$662$$ 0 0
$$663$$ −27348.0 −1.60197
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −28016.0 −1.62636
$$668$$ 0 0
$$669$$ 5052.00 0.291961
$$670$$ 0 0
$$671$$ −112.000 −0.00644368
$$672$$ 0 0
$$673$$ −7962.00 −0.456036 −0.228018 0.973657i $$-0.573225\pi$$
−0.228018 + 0.973657i $$0.573225\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −12226.0 −0.694067 −0.347033 0.937853i $$-0.612811\pi$$
−0.347033 + 0.937853i $$0.612811\pi$$
$$678$$ 0 0
$$679$$ 18520.0 1.04673
$$680$$ 0 0
$$681$$ −6012.00 −0.338297
$$682$$ 0 0
$$683$$ −8748.00 −0.490092 −0.245046 0.969511i $$-0.578803\pi$$
−0.245046 + 0.969511i $$0.578803\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 15126.0 0.840019
$$688$$ 0 0
$$689$$ 10836.0 0.599156
$$690$$ 0 0
$$691$$ 7324.00 0.403210 0.201605 0.979467i $$-0.435384\pi$$
0.201605 + 0.979467i $$0.435384\pi$$
$$692$$ 0 0
$$693$$ 10080.0 0.552536
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −26076.0 −1.41707
$$698$$ 0 0
$$699$$ −9270.00 −0.501607
$$700$$ 0 0
$$701$$ −21934.0 −1.18179 −0.590896 0.806748i $$-0.701226\pi$$
−0.590896 + 0.806748i $$0.701226\pi$$
$$702$$ 0 0
$$703$$ 1128.00 0.0605168
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −3960.00 −0.210652
$$708$$ 0 0
$$709$$ −10690.0 −0.566250 −0.283125 0.959083i $$-0.591371\pi$$
−0.283125 + 0.959083i $$0.591371\pi$$
$$710$$ 0 0
$$711$$ −3672.00 −0.193686
$$712$$ 0 0
$$713$$ 20672.0 1.08580
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 6408.00 0.333767
$$718$$ 0 0
$$719$$ −13792.0 −0.715375 −0.357688 0.933841i $$-0.616435\pi$$
−0.357688 + 0.933841i $$0.616435\pi$$
$$720$$ 0 0
$$721$$ −30640.0 −1.58265
$$722$$ 0 0
$$723$$ −294.000 −0.0151231
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −24004.0 −1.22457 −0.612283 0.790639i $$-0.709749\pi$$
−0.612283 + 0.790639i $$0.709749\pi$$
$$728$$ 0 0
$$729$$ 729.000 0.0370370
$$730$$ 0 0
$$731$$ 43672.0 2.20967
$$732$$ 0 0
$$733$$ −8562.00 −0.431439 −0.215719 0.976455i $$-0.569210\pi$$
−0.215719 + 0.976455i $$0.569210\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −21728.0 −1.08597
$$738$$ 0 0
$$739$$ 13836.0 0.688722 0.344361 0.938837i $$-0.388096\pi$$
0.344361 + 0.938837i $$0.388096\pi$$
$$740$$ 0 0
$$741$$ 1032.00 0.0511626
$$742$$ 0 0
$$743$$ −22224.0 −1.09733 −0.548667 0.836041i $$-0.684865\pi$$
−0.548667 + 0.836041i $$0.684865\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 6012.00 0.294468
$$748$$ 0 0
$$749$$ −8880.00 −0.433202
$$750$$ 0 0
$$751$$ −11544.0 −0.560914 −0.280457 0.959867i $$-0.590486\pi$$
−0.280457 + 0.959867i $$0.590486\pi$$
$$752$$ 0 0
$$753$$ −15120.0 −0.731744
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 3814.00 0.183120 0.0915602 0.995800i $$-0.470815\pi$$
0.0915602 + 0.995800i $$0.470815\pi$$
$$758$$ 0 0
$$759$$ −22848.0 −1.09266
$$760$$ 0 0
$$761$$ −25662.0 −1.22240 −0.611200 0.791476i $$-0.709313\pi$$
−0.611200 + 0.791476i $$0.709313\pi$$
$$762$$ 0 0
$$763$$ 1240.00 0.0588349
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −4816.00 −0.226722
$$768$$ 0 0
$$769$$ 30658.0 1.43765 0.718827 0.695189i $$-0.244679\pi$$
0.718827 + 0.695189i $$0.244679\pi$$
$$770$$ 0 0
$$771$$ −5958.00 −0.278304
$$772$$ 0 0
$$773$$ 30894.0 1.43749 0.718745 0.695274i $$-0.244717\pi$$
0.718745 + 0.695274i $$0.244717\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 16920.0 0.781212
$$778$$ 0 0
$$779$$ 984.000 0.0452573
$$780$$ 0 0
$$781$$ 37632.0 1.72417
$$782$$ 0 0
$$783$$ 5562.00 0.253857
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 21596.0 0.978163 0.489081 0.872238i $$-0.337332\pi$$
0.489081 + 0.872238i $$0.337332\pi$$
$$788$$ 0 0
$$789$$ −4248.00 −0.191677
$$790$$ 0 0
$$791$$ −8280.00 −0.372191
$$792$$ 0 0
$$793$$ −172.000 −0.00770227
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 8646.00 0.384262 0.192131 0.981369i $$-0.438460\pi$$
0.192131 + 0.981369i $$0.438460\pi$$
$$798$$ 0 0
$$799$$ 4240.00 0.187735
$$800$$ 0 0
$$801$$ 594.000 0.0262022
$$802$$ 0 0
$$803$$ −65520.0 −2.87939
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 20010.0 0.872844
$$808$$ 0 0
$$809$$ 24954.0 1.08447 0.542235 0.840227i $$-0.317578\pi$$
0.542235 + 0.840227i $$0.317578\pi$$
$$810$$ 0 0
$$811$$ −40004.0 −1.73210 −0.866048 0.499960i $$-0.833348\pi$$
−0.866048 + 0.499960i $$0.833348\pi$$
$$812$$ 0 0
$$813$$ 144.000 0.00621193
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −1648.00 −0.0705707
$$818$$ 0 0
$$819$$ 15480.0 0.660458
$$820$$ 0 0
$$821$$ 16570.0 0.704381 0.352191 0.935928i $$-0.385437\pi$$
0.352191 + 0.935928i $$0.385437\pi$$
$$822$$ 0 0
$$823$$ −4388.00 −0.185852 −0.0929259 0.995673i $$-0.529622\pi$$
−0.0929259 + 0.995673i $$0.529622\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 14364.0 0.603972 0.301986 0.953312i $$-0.402350\pi$$
0.301986 + 0.953312i $$0.402350\pi$$
$$828$$ 0 0
$$829$$ −21170.0 −0.886929 −0.443465 0.896292i $$-0.646251\pi$$
−0.443465 + 0.896292i $$0.646251\pi$$
$$830$$ 0 0
$$831$$ 20814.0 0.868868
$$832$$ 0 0
$$833$$ 6042.00 0.251312
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −4104.00 −0.169480
$$838$$ 0 0
$$839$$ −10664.0 −0.438811 −0.219405 0.975634i $$-0.570412\pi$$
−0.219405 + 0.975634i $$0.570412\pi$$
$$840$$ 0 0
$$841$$ 18047.0 0.739965
$$842$$ 0 0
$$843$$ 5082.00 0.207632
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 36100.0 1.46448
$$848$$ 0 0
$$849$$ 19092.0 0.771774
$$850$$ 0 0
$$851$$ −38352.0 −1.54488
$$852$$ 0 0
$$853$$ 3190.00 0.128046 0.0640232 0.997948i $$-0.479607\pi$$
0.0640232 + 0.997948i $$0.479607\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −20814.0 −0.829630 −0.414815 0.909906i $$-0.636154\pi$$
−0.414815 + 0.909906i $$0.636154\pi$$
$$858$$ 0 0
$$859$$ 18988.0 0.754205 0.377103 0.926172i $$-0.376920\pi$$
0.377103 + 0.926172i $$0.376920\pi$$
$$860$$ 0 0
$$861$$ 14760.0 0.584227
$$862$$ 0 0
$$863$$ 11664.0 0.460078 0.230039 0.973181i $$-0.426115\pi$$
0.230039 + 0.973181i $$0.426115\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −18969.0 −0.743046
$$868$$ 0 0
$$869$$ −22848.0 −0.891905
$$870$$ 0 0
$$871$$ −33368.0 −1.29808
$$872$$ 0 0
$$873$$ 8334.00 0.323096
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 8246.00 0.317500 0.158750 0.987319i $$-0.449254\pi$$
0.158750 + 0.987319i $$0.449254\pi$$
$$878$$ 0 0
$$879$$ −9402.00 −0.360775
$$880$$ 0 0
$$881$$ 22890.0 0.875350 0.437675 0.899133i $$-0.355802\pi$$
0.437675 + 0.899133i $$0.355802\pi$$
$$882$$ 0 0
$$883$$ 33548.0 1.27857 0.639287 0.768969i $$-0.279230\pi$$
0.639287 + 0.768969i $$0.279230\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −32264.0 −1.22133 −0.610665 0.791889i $$-0.709098\pi$$
−0.610665 + 0.791889i $$0.709098\pi$$
$$888$$ 0 0
$$889$$ −19920.0 −0.751513
$$890$$ 0 0
$$891$$ 4536.00 0.170552
$$892$$ 0 0
$$893$$ −160.000 −0.00599574
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −35088.0 −1.30608
$$898$$ 0 0
$$899$$ −31312.0 −1.16164
$$900$$ 0 0
$$901$$ 13356.0 0.493843
$$902$$ 0 0
$$903$$ −24720.0 −0.910997
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 51228.0 1.87541 0.937706 0.347431i $$-0.112946\pi$$
0.937706 + 0.347431i $$0.112946\pi$$
$$908$$ 0 0
$$909$$ −1782.00 −0.0650222
$$910$$ 0 0
$$911$$ 2144.00 0.0779735 0.0389868 0.999240i $$-0.487587\pi$$
0.0389868 + 0.999240i $$0.487587\pi$$
$$912$$ 0 0
$$913$$ 37408.0 1.35600
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 5280.00 0.190143
$$918$$ 0 0
$$919$$ −33584.0 −1.20548 −0.602739 0.797939i $$-0.705924\pi$$
−0.602739 + 0.797939i $$0.705924\pi$$
$$920$$ 0 0
$$921$$ 708.000 0.0253305
$$922$$ 0 0
$$923$$ 57792.0 2.06094
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −13788.0 −0.488519
$$928$$ 0 0
$$929$$ −3590.00 −0.126786 −0.0633929 0.997989i $$-0.520192\pi$$
−0.0633929 + 0.997989i $$0.520192\pi$$
$$930$$ 0 0
$$931$$ −228.000 −0.00802621
$$932$$ 0 0
$$933$$ 11328.0 0.397494
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 21686.0 0.756084 0.378042 0.925788i $$-0.376597\pi$$
0.378042 + 0.925788i $$0.376597\pi$$
$$938$$ 0 0
$$939$$ −23754.0 −0.825540
$$940$$ 0 0
$$941$$ −5174.00 −0.179243 −0.0896215 0.995976i $$-0.528566\pi$$
−0.0896215 + 0.995976i $$0.528566\pi$$
$$942$$ 0 0
$$943$$ −33456.0 −1.15533
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 35524.0 1.21898 0.609490 0.792793i $$-0.291374\pi$$
0.609490 + 0.792793i $$0.291374\pi$$
$$948$$ 0 0
$$949$$ −100620. −3.44179
$$950$$ 0 0
$$951$$ 13086.0 0.446207
$$952$$ 0 0
$$953$$ 16122.0 0.547999 0.273999 0.961730i $$-0.411653\pi$$
0.273999 + 0.961730i $$0.411653\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 34608.0 1.16898
$$958$$ 0 0
$$959$$ −45560.0 −1.53411
$$960$$ 0 0
$$961$$ −6687.00 −0.224464
$$962$$ 0 0
$$963$$ −3996.00 −0.133717
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 19188.0 0.638102 0.319051 0.947738i $$-0.396636\pi$$
0.319051 + 0.947738i $$0.396636\pi$$
$$968$$ 0 0
$$969$$ 1272.00 0.0421698
$$970$$ 0 0
$$971$$ 38464.0 1.27123 0.635617 0.772004i $$-0.280746\pi$$
0.635617 + 0.772004i $$0.280746\pi$$
$$972$$ 0 0
$$973$$ −36240.0 −1.19404
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 43930.0 1.43853 0.719266 0.694735i $$-0.244478\pi$$
0.719266 + 0.694735i $$0.244478\pi$$
$$978$$ 0 0
$$979$$ 3696.00 0.120659
$$980$$ 0 0
$$981$$ 558.000 0.0181606
$$982$$ 0 0
$$983$$ 17328.0 0.562235 0.281118 0.959673i $$-0.409295\pi$$
0.281118 + 0.959673i $$0.409295\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −2400.00 −0.0773990
$$988$$ 0 0
$$989$$ 56032.0 1.80153
$$990$$ 0 0
$$991$$ 18160.0 0.582110 0.291055 0.956706i $$-0.405994\pi$$
0.291055 + 0.956706i $$0.405994\pi$$
$$992$$ 0 0
$$993$$ 23940.0 0.765068
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 9102.00 0.289131 0.144565 0.989495i $$-0.453822\pi$$
0.144565 + 0.989495i $$0.453822\pi$$
$$998$$ 0 0
$$999$$ 7614.00 0.241137
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1200.4.a.p.1.1 1
4.3 odd 2 600.4.a.i.1.1 1
5.2 odd 4 1200.4.f.t.49.2 2
5.3 odd 4 1200.4.f.t.49.1 2
5.4 even 2 240.4.a.g.1.1 1
12.11 even 2 1800.4.a.f.1.1 1
15.14 odd 2 720.4.a.q.1.1 1
20.3 even 4 600.4.f.a.49.2 2
20.7 even 4 600.4.f.a.49.1 2
20.19 odd 2 120.4.a.b.1.1 1
40.19 odd 2 960.4.a.bj.1.1 1
40.29 even 2 960.4.a.k.1.1 1
60.23 odd 4 1800.4.f.v.649.2 2
60.47 odd 4 1800.4.f.v.649.1 2
60.59 even 2 360.4.a.n.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.a.b.1.1 1 20.19 odd 2
240.4.a.g.1.1 1 5.4 even 2
360.4.a.n.1.1 1 60.59 even 2
600.4.a.i.1.1 1 4.3 odd 2
600.4.f.a.49.1 2 20.7 even 4
600.4.f.a.49.2 2 20.3 even 4
720.4.a.q.1.1 1 15.14 odd 2
960.4.a.k.1.1 1 40.29 even 2
960.4.a.bj.1.1 1 40.19 odd 2
1200.4.a.p.1.1 1 1.1 even 1 trivial
1200.4.f.t.49.1 2 5.3 odd 4
1200.4.f.t.49.2 2 5.2 odd 4
1800.4.a.f.1.1 1 12.11 even 2
1800.4.f.v.649.1 2 60.47 odd 4
1800.4.f.v.649.2 2 60.23 odd 4